The shifted fractional trapezoidal rule (SFTR) with a special shift is adopted to construct a finite difference scheme for the time-fractional Allen-Cahn (tFAC) equation. Some essential key properties of the weights of SFTR are explored for the first time. Based on these properties, we rigorously demonstrate the discrete energy decay property and maximum-principle preservation for the scheme. Numerical investigations show that the scheme can resolve the intrinsic initial singularity of such nonlinear fractional equations as tFAC equation on uniform meshes without any correction. Comparison with the classic fractional BDF2 and L2-1$_\sigma$ method further validates the superiority of SFTR in solving the tFAC equation. Experiments concerning both discrete energy decay and discrete maximum-principle also verify the correctness of the theoretical results.
翻译:采用带有特殊变换的分数捕捉自毁规则(SFTR)来为时间折射Allen-Cahn(tFAC)方程式构建一个限定的差别方案。 第一次探索SFTR重量的一些关键特性。 基于这些特性, 我们严格地展示离散能源衰减特性和该办法的最大原则保全。 数字调查显示, 方案可以解决非线性分数方程式的内在初始奇特性, 如单项单项单项单项单项单项, 不作任何校正 。 与经典的分数 BDF2 和 L2-1$ <unk> gag$ 方法相比, 进一步验证SFTR在解决tFAC方程式中的优越性。 有关离散能源衰减和离散最大原则的实验也验证了理论结果的正确性 。</s>